Computation of empirical eigenfunctions and order reduction for nonlinear parabolic PDE systems with time-dependent spatial domains

This article presents a methodology for the computation of empirical eigenfunctions and the construction of accurate low-dimensional approximations for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. The method is successfully applied to a diffusion-reaction process with nonlinearities, spatially-varying coefficients and time-dependent spatial domain, and is shown to lead to the construction of accurate low-order models that are robust with respect to variations in the model parameters and different initial conditions.